The freezing method for Volterra integral equations in a Banach space
The "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type $$ x(t)- \int_0^t K(t, t-s)x(s)ds =f(t)\;(t\geq 0),$$ where $K(t,s)$ is an operator valued function "slowly" varying in the first argument. Bes...
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| Format: | Article |
| Language: | English |
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University of Szeged
2008-04-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=307 |
| _version_ | 1797830795059003392 |
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| author | Michael Gil' |
| author_facet | Michael Gil' |
| author_sort | Michael Gil' |
| collection | DOAJ |
| description | The "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type $$ x(t)- \int_0^t K(t, t-s)x(s)ds =f(t)\;(t\geq 0),$$ where $K(t,s)$ is an operator valued function "slowly" varying in the first argument. Besides, sharp explicit stability conditions are derived. |
| first_indexed | 2024-04-09T13:41:50Z |
| format | Article |
| id | doaj.art-9a9520fdb40347019dc56c30c3c8e7b4 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:50Z |
| publishDate | 2008-04-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-9a9520fdb40347019dc56c30c3c8e7b42023-05-09T07:52:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752008-04-012008171710.14232/ejqtde.2008.1.17307The freezing method for Volterra integral equations in a Banach spaceMichael Gil'0Department of Mathematics, Ben-Gurion University of the Negev, IsraelThe "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type $$ x(t)- \int_0^t K(t, t-s)x(s)ds =f(t)\;(t\geq 0),$$ where $K(t,s)$ is an operator valued function "slowly" varying in the first argument. Besides, sharp explicit stability conditions are derived.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=307 |
| spellingShingle | Michael Gil' The freezing method for Volterra integral equations in a Banach space Electronic Journal of Qualitative Theory of Differential Equations |
| title | The freezing method for Volterra integral equations in a Banach space |
| title_full | The freezing method for Volterra integral equations in a Banach space |
| title_fullStr | The freezing method for Volterra integral equations in a Banach space |
| title_full_unstemmed | The freezing method for Volterra integral equations in a Banach space |
| title_short | The freezing method for Volterra integral equations in a Banach space |
| title_sort | freezing method for volterra integral equations in a banach space |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=307 |
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